curve #2505

y² + xy + y = x³ − 126444634x + 334325609996

a-invariants: [1, 0, 1, -126444634, 334325609996]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 178710
discriminant (Δ): 81094935915800986742841600
Faltings height: 3.6720
naive height: 67.5795
primes of bad reduction: 2, 3, 5, 7, 23, 37
regulator: 5.304874192082891415495876555442050333670
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:46 UTC
last updated: 2026-09-26 20:05:46 UTC

Witness: 1 independent point log in to add more points →

(1165, 433697)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=7; A=(3q-p)(p+q)^3=-26973, B=-(p+3q)(p-q)^3=60835. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 20:05:46 UTC · history